Chapter 1 Introduction to Probability 1
1.1 Introduction 1
1.2 Interpretations of Probability 3
1.3 Set Algebra 6
1.4 The Definition of Probability 9
1.5 Finite Sample Spaces 12
1.6 Geometry Probability Setting 17
1.7 Conditional Probability 20
1.8 Independent Events 26
Chapter 2 Random Variable and Distribution 34
2.1 Random Variable 34
2.2 Discrete Distribution 40
2.3 Continuous Random Variable and Its Distribution 48
2.4 The Function of a Random Variable 58
Chapter 3 Multi-Dimensional Random Variable and Distributions 65
3.1 Multi-Dimensional Random Variable and its Distribution 65
3.2 Marginal Distribution 74
3.3 Conditional Distribution 80
3.4 Independence of Random Variables 85
3.5 Functions of TWo or More Random Variables 90
Chapter 4 Expectation 103
4.1 Expectation of Random Variable 103
4.2 Variance and Moments 115
4.3 Covariance and Correlation 125
4.4 Covariance Matrix 131
Chapter 5 Limit Theorem 139
5.1 Law of Large Numbers 139
5.2 the Central Limit Theorem 143
Chapter 6 Samples and Sampling Distribution 149
6.1 Random Samples 149
6.2 Statistics and Numerical Characteristics of Sample 152
6.3 Sampling Distribution 155
6.4 Distributions of Sample Mean and Sample Variance with Normal Distribution 168
Chapter 7 Estimation of Parameters 178
7.1 Point Estimation,Moment Estimation and Maximum Likehood Estimators 178
7.2 the Evaluation Criteria of Estimators 193
7.3 Estimation of Intervals 200
7.4 Interval Estimation of Normal Population Parameters 203
7.5 One-Sided Confidence Interval 209
Chapter 8 Testing Hypotheses 217
8.1 Problem of Testing Hypotheses 217
8.2 the Testing of Hypotheses of the Mean of the Normal Distribution 223
8.3 Testing Hypotheses about Variance of Normal Distribution 231
8.4 Equivalence of Tests and Confidence Sets 235
8.5 Test of Fit of Population Distribution 236
8.6 Testing of Hypotheses Using P-value 240
Chapter 9 Simple Linear Regression 246
9.1 the Method of Regression 246
9.2 Estimation and Inference in Simple Linear Regression 252
Solutions for Exercises 286
References 304
- 《概率统计高级教程 英文 统计学的概率基础》（美）源亨，（美）王通会编著 2008
- 《概率论与数理统计 英文》毛纲源，徐丽莉主编 2017
- 《概率统计 英文版》（美）stone，C.J.著 2003
- 《概率与统计 英文版》（美）沃波尔等著 2013
- 《概率论与数理统计=PROBABILITY AND STATSTICS 英文》孔令臣 2015
- 《概率统计 原书第4版 英文版》（美）德格鲁特，（美）舍维什著 2012
- 《概率论与数理统计 英文》孔令臣，王立春编著 2015
- 《概率论与数理统计 第9版 英文版=PROBABILITY AND STATISTICS FOR ENGINEERS》NINTH EDITION 2017
- 《概率、统计与随机过程 第4版 英文版》（美）亨利·斯塔克，（美）伍兹著 2012
- 《Miller & Freund's probability and statistics for engineers Seventh Edition = 概率论与数理统计 英文版 第七版》Richard A. Johnson 2005
